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Math Help - I'm stuck with simple DE

  1. #1
    Newbie
    Joined
    Apr 2010
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    1

    I'm stuck with simple DE

    Hi!
    Could someone please help me. I don't know how to solve this DE and I have exams coming up tomorrow....

    (xy )d/dx = (y^2)*(x^1/2) , with the condition y(1) = 1.

    I would be most grateful for any help.

    Best regards,
    Sara
    [IMG]file:///C:/DOCUME%7E1/SARASE%7E1/LOCALS%7E1/Temp/moz-screenshot-2.png[/IMG]
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  2. #2
    Senior Member
    Joined
    Feb 2010
    Posts
    422
    Do you mean xy\dot{y}=y^2\sqrt{x}?

    If so, it is seperable to {\mathrm{d}y\over y} = {\mathrm{d}x\over\sqrt{x}}, which can be solved by integrating from 1 to x.

    [Another method is to multiply by an integrating factor h and rearrange to get h\sqrt{x}y\dot{y}-hy^2=0, and then look for a function g s.t. the LHS is =\frac{\mathrm{d}}{\mathrm{d}x}(gy^2) = \dot{g}y^2 + 2gy\dot{y} by equating coefficients of like terms, but this is probably harder so I'm not sure why I mentioned it........ ]

    Anyway, check your formula, I think it might have a typo.

    P.S. Images must be located by a URL, so for instance, the local path to an image on your personal machine will not do.
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